equal
deleted
inserted
replaced
441 \] |
441 \] |
442 Here $C_*$ means singular chains and $\Homeo_\bd(X)$ is the space of homeomorphisms of $X$ |
442 Here $C_*$ means singular chains and $\Homeo_\bd(X)$ is the space of homeomorphisms of $X$ |
443 which fix $\bd X$. |
443 which fix $\bd X$. |
444 These action maps are required to be associative up to homotopy |
444 These action maps are required to be associative up to homotopy |
445 \nn{iterated homotopy?}, and also compatible with composition (gluing) in the sense that |
445 \nn{iterated homotopy?}, and also compatible with composition (gluing) in the sense that |
446 a diagram like the one in Proposition \ref{CDprop} commutes. |
446 a diagram like the one in Proposition \ref{CHprop} commutes. |
447 \nn{repeat diagram here?} |
447 \nn{repeat diagram here?} |
448 \nn{restate this with $\Homeo(X\to X')$? what about boundary fixing property?} |
448 \nn{restate this with $\Homeo(X\to X')$? what about boundary fixing property?} |
449 \end{axiom-numbered} |
449 \end{axiom-numbered} |
450 |
450 |
451 We should strengthen the above axiom to apply to families of extended homeomorphisms. |
451 We should strengthen the above axiom to apply to families of extended homeomorphisms. |
965 \] |
965 \] |
966 Here $C_*$ means singular chains and $\Homeo_\bd(M)$ is the space of homeomorphisms of $M$ |
966 Here $C_*$ means singular chains and $\Homeo_\bd(M)$ is the space of homeomorphisms of $M$ |
967 which fix $\bd M$. |
967 which fix $\bd M$. |
968 These action maps are required to be associative up to homotopy |
968 These action maps are required to be associative up to homotopy |
969 \nn{iterated homotopy?}, and also compatible with composition (gluing) in the sense that |
969 \nn{iterated homotopy?}, and also compatible with composition (gluing) in the sense that |
970 a diagram like the one in Proposition \ref{CDprop} commutes. |
970 a diagram like the one in Proposition \ref{CHprop} commutes. |
971 \nn{repeat diagram here?} |
971 \nn{repeat diagram here?} |
972 \nn{restate this with $\Homeo(M\to M')$? what about boundary fixing property?}} |
972 \nn{restate this with $\Homeo(M\to M')$? what about boundary fixing property?}} |
973 |
973 |
974 \medskip |
974 \medskip |
975 |
975 |